两个（或多个）h 的故事
A tale of two (or more) $h$'s
AI总结：
本文利用BOSS和eBOSS大尺度结构数据结合BBN丰度，通过BAO+BBN和功率谱形状+BBN两种方法测量哈勃常数，发现二者在ΛCDM内一致，并指出解决哈勃张力的模型须同时修改声视界和物质-辐射相等尺度物理。
摘要：
我们利用来自 BOSS 和 eBOSS 巡天的大尺度结构星系数据（LSS），并结合大爆炸核合成（BBN）的丰度信息，来测量两个哈勃膨胀率的值，$H_0=100h\,[{\ m km}\, {\ m s}^{-1}\,{\ m Mpc}^{-1}]$，每一个都基于非常不同的物理过程。一个是（传统的）晚期背景测量，基于确定 BAO 尺度并利用 BBN 的重子丰度来校准其绝对大小（BAO+BBN）。该方法将 $H_0$ 锚定在复合前时期声视界尺度的（标准）物理上。另一个是较新的早期测量，与功率谱的宽带形状相关。这第二种方法将 $H_0$ 锚定在物质-辐射相等尺度的物理上，它也需要 BBN 信息来确定功率谱形状中重子的抑制（shape+BBN）。在 $Λ$CDM 模型内，我们发现这两个 $H_0$ 之间具有非常好的一致性：BAO+BBN（+growth）给出 $H_0=67.42_{-0.94}^{+0.88}$ $(67.37_{-0.95}^{+0.86})$ km s$^{-1}$Mpc$^{-1}$，而 shape+BBN（+growth）给出 $H_0 = 70.1_{-2.1}^{+2.1}$ $(70.1_{-2.1}^{+1.9})$ km s$^{-1}$ Mpc$^{-1}$，其中“growth”代表由结构增长参数捕获的晚期扰动信息。这些是迄今为止来自 LSS 数据的最严格的无声视界 $H_0$ 约束。因此，为了可行，任何为解决所谓“哈勃张力”而提出的 $Λ$CDM 扩展都需要一致地修改不仅声视界尺度物理，还要修改物质-辐射相等尺度，以使晚期和早期基于的 $H_0$ 都返回相互一致的结果，并与标准宇宙距离阶梯（距离-红移关系）测定所恢复的高 $H_0$ 值一致。
英文摘要：
We use the large-scale structure galaxy data (LSS) from the BOSS and eBOSS surveys, in combination with abundances information from Big Bang Nucleosynthesis (BBN) to measure two values of the Hubble expansion rate, $H_0=100h\,[{\rm km}\, {\rm s}^{-1}\,{\rm Mpc}^{-1}]$, each of them based on very different physical processes. One is a (traditional) late-time-background measurement based on determining the BAO scale and using BBN abundances on baryons for calibrating its absolute size (BAO+BBN). This method anchors $H_0$ to the (standard) physics of the sound horizon scale at pre-recombination times. The other is a newer early-time based measurement associated with the broadband shape of the power spectrum. This second method anchors $H_0$ to the physics of the matter-radiation equality scale, which also needs BBN information for determining the suppression of baryons in the power spectrum shape (shape+BBN). Within the $Λ$CDM model, we find very good consistency among these two $H_0$'s: BAO+BBN (+growth) delivers $H_0=67.42_{-0.94}^{+0.88}$ $(67.37_{-0.95}^{+0.86})$ km s$^{-1}$Mpc$^{-1}$ , whereas the shape+BBN (+growth) delivers $H_0 = 70.1_{-2.1}^{+2.1}$ $(70.1_{-2.1}^{+1.9})$ km s$^{-1}$ Mpc$^{-1}$, where "growth" stands for information from the late-time-perturbations captured by the growth of structure parameter. These are the tightest sound-horizon free $H_0$ constraints from LSS data to date. As a consequence to be viable, any $Λ$CDM extension proposed to address the so-called "Hubble tension" needs to modify consistently not only the sound horizon scale physics, but also the matter-radiation equality scale, in such a way that both late- and early-based $H_0$'s return results mutually consistent and consistent with the high $H_0$ value recovered by the standard cosmic distance ladder (distance-redshift relation) determinations.
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